The overnight attack on the Starokozache road crossing, about 500km south of Kyiv, also wounded three others, according to Odesa regional head Oleh Kiper. Images from the scene showed several burnt-out cars among debris. The crossing has been closed.
A Moldovan driver was among the injured, Moldova's foreign ministry confirmed. Moldova has increasingly found itself caught up in the conflict, with Prime Minister Vasile Tofan saying 17 drones struck Moldovan territory in August alone — more than during the whole of last year.
"Those who ignore or downplay these threats — and refuse to name the aggressor — are denying reality," Tofan wrote on social media. "Russia started this war. Russia alone bears responsibility."
In the Ukrainian capital Kyiv, a woman was killed and 14 people, including two children, were injured when a Russian drone hit a nine-storey residential building, officials said.
In Russia, four people, including a child, were killed in a Ukrainian drone attack on the Black Sea port of Novorossiysk, according to Russian officials. A drone also struck an industrial facility in the Arctic city of Novy Urengoy, nearly 3,000km from Ukraine.
Zelensky renewed calls for international support, saying "the aggression must be stopped here and now before it spreads any further."
Russia launched its full-scale invasion of Ukraine in February 2022. Both sides have recently stepped up long-range strikes despite ongoing diplomatic initiatives to end the war.